Molecular ion beam method of isotopic analysis: Effect of error propagation, a case study with Li₂BO

Abstract

The isotopic analysis of boron has been carried out using dflerent pairs of isotopic Li2BO: ions as monitors. The precision of the mass spectrometric measurements of different molecular abundance ratios is roughly the same. However, the values of the '%/"B abundance ratio calculated from the experimental ratios of different pairs of isotopic molecular ions show large variations. These variations are shown to be a logical consequence of the calculation step which leads to the magnification of measurement errors to different extents for different peak ratios. Similar arguments would apply for the isotopic analysis of any element employing the molecular ion beam technique. The effect of isotopic fractionation on the molecular abundances is also discussed. The important implication of the present investigation is that it sets the guidelines for selecting suitable monitor molecules to avoid such errors.Molecular ion beams are sometimes employed for the isotopic analysis of elements. ' -12 The related analytical procedure is, by and large, comparable to the conventional atomic ion beam method of isotopic analysis. However, the molecular ion beam method involves (barring those cases where all other constituents of the chosen molecule except the element of interest are monoisotopic) calculations of elemental isotopic abundance ratio(s) from the experimentally measured molecular ion ratio(s) using known isotopic abundance values of the other constituent elements. The central theme of this paper is to pay attention to this calculation step. This is because the calculation process may either enhance or even reduce the error in isotopic analysis due to error propagation, as indicated in Ref.12 which dealt with the determination of the 6Li/7Li abundance ratio using the Li2B02 molecule with all constituent isotopes at their natural isotopic abundance. It was demonstrated" that the precision of the measurements of the intensity ratio of the most abundant Li,BO: ions (mlz 56 and 57) is better than 0.1% , while the uncertainty in the value determined for the 6Li/7Li abundance ratio is 0.3%. The present work involves the isotopic analysis of a "B-enriched isotopic reference material of boron, SRM-952. This was chosen with a view to examining whether the selection of the most abundant Li,BO: ions as monitors also ensures accurate isotopic analysis of a constituent element whose isotopic abundance ratios are quite different from the natural ratios. This paper presents the loB/'lB abundance ratios determined using the experimental intensity ratios of different pairs of isotopic molecular ions and discusses the differences in the results so obtained. EXPERIMENTALThe instrument used is a thermal ionization mass spectrometer, model 261 (Finnigan MAT, Bremen, Germany), upgraded for simultaneous collection of separated ion beams.Author to whom correspondence should be addressed.The lithium sample used for this work was Li2C03, a natural isotopic standard of lithium Svec with certified 6Li/7Li abundance ratio of 0.0832 k 0.0002. l3 The ...

Error-systematics of determining elemental isotopic abundance ratios by the molecular ion beam method: a case study for the simultaneous isotopic analysis of lithium and boron as Li2BO2+

“…Secondly their magnitudes, even for given measurement errors, will depend on the particular isotopic molecular ion‐pairs employed as the monitor pairs. These results thus imply that “judicious selection of monitor pairs”16–18 should be a necessary requirement for ensuring beforehand that the determined isotopic abundance ratios (L and Y) would be not only correct but be as accurate as desired. The present findings may, therefore, be regarded as an extension of the observations which have already demonstrated16–18 that the accuracy of isotopic analysis by the molecular ion beam method is governed by error‐propagation rather than by the accuracy of measurements.…”

“…For the isotopic analysis of elements, the measurements of different isotopic abundance ratios (E i 's) are sometimes carried out indirectly, by employing suitable molecular ions of the analyte element(s) as the monitors for measurements,1–20 and the technique is referred as the molecular ion beam method (MIBM). The advantage of this method (over the conventional atomic ion beam method) is that one can determine E i 's of more than one element by a single experimental exercise.…”

“…Since the ratio R i measurements are made on peaks of chosen isotopic $\hbox{Li}_{2}\hbox{BO}_{2}^{+}$ ions, the required relationships (Eqns 3 and 4) can be exactly defined,15–19 and solved for L and Y.…”

“…1 with i = 1). The corresponding accuracy of analysis is given as follows:16–18 where $[\hbox{REMF}]_{\rm R}^{\rm E}$ is called the relative error magnification factor. That is, The superscript “E” stands for a given E i to be determined (e.g.…”

Error‐systematics of determining simultaneously the isotopic abundance ratios of natural lithium and natural boron as Li 2 BO 2 +

“…Now, however, we consider the case of determining any single E i at a time by the molecular ion beam method3–17 (MIBM), e.g. either L or Y as $\hbox{Li}_{2}\hbox{BO}_{2}^{+}$ .…”